Consider a gravity-free hall in which an experimenter of mass 50 kg is resting on a 5 kg pillow, 8 ft above the flooe of the hall. He pushes the pillow down so that it starts falling at a speed of 8ft/s. The pillow makes a perfectly elastic collision with the floow, rebounds and reaches the experimenter's head. Find the time elaspsed in the process.

Explanation

mass of the man `(M_m)=50kg`
mass of the pillow `(M_p)=5kg`
When the pillow is pushed by the man the pillow will go down while the man goes up.
It becomes the exterN/Al force on the system which is zero
`rarr `acceleration of centre of mass is zero.
velocity of centre of mass is constant
`:. M_mxxV_m=M_pxxV_p`.......i
Giventhe velocity of pillow ils 80 fg/s
which is relative velocity of pillow w.r.t man
`V_(p/m)=v_p-(-Vm)`
`=V+Vm`
`rarr V_p=V_p/m-V_m`
putting in equation i
`M_x xxV_m=M_pxx(V-(p/m)-V_m)`
`rarr 50xxV_m=5x(8-V_m)`
`V_mk=8/11=0.727ft/s`
`:.` Absolute velocity of pillow ltbr.`=8-0.727=7.2t/sec`
`:.` Time taken to reach the floor
`=s/v=8/7.2=1.1sec`
As the mass of wallgtgtgtthen pillow.
The velocity of block before the collision.
=velocity after the collisioin
`rarr time of ascent =1.11sec.
`:.` Total time taken =1.11+1.11=2.22sec`.